Please help me with this question Experts please

Dear student,

We consider a Gaussian surface of a pill box extremely small length and extremely small cross-section as σ.
A fraction of it ls inside the surface and tht remaining part is outside the surface.

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The total charge enclosed by this pill box is q =σ ds
where σ = surface charge density of conductor.
At every point on the surface of the conductor E is perpendicular to the surface. Hence, it is parallel to the surface vector E∣∣ds
But inside the surface E=0 .
Hence, the flux coming out from the cross-section of pill box inside the surface=0
The flux coming out from the cross-section of pill box outside the surface,
$$\begin{gathered} \varphi =E.ds = E ds \cos 0 = Eds \\ According to Gauss.s therorem \varphi =Eds \\ \therefore \frac{q}{{\epsilon }_0}= Eds \\ \therefore \frac{\sigma ds}{{\epsilon }_0}= Eds \\ \therefore E=\frac{\sigma }{{\epsilon }_0} \end{gathered}$$

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